They wanted to make their own nation in their own place. They had developed different cultures and ways of life since then, and wanted freedom. One of the other reasons of the revolution was the taxes on them, and because they had no representation of the Parliament that was ruling them. Many people came from Britain to the Americas to get away and start a new life, and many came for religious freedom.

This was generally not a war of cultures since American and British citizenry were extremely similar. It was (very simplistically) an issue of taxation and representation. During the 7 Years War, also known as the French and Indian War, Britain spent a large sum on protecting and defending its colonies throughout America from the French. This war was a massive drain on the British economy and to help recover they decided to tax the American colonies more heavily than before since much of that expense had come specifically from defending the colonies themselves.

Even after the war there were substantial factions on both sides who assumed the two would be reunited again eventually due to the cultures and citizens being essentially one and the same. This is all of course a very simplistic explanation and of there are tons of nuances on each side.

The Americans were rooted in British culture, but had very much become their own nation, if not their own state, in the roughly 150 years of the first permanent settlements:

1. The Americans had their own view of who was gentry (or who could vote, basically,) and this was massively more broad than what the British would ever accept.

2. The Americans saw fighting in war as a patriotic demonstration, which was not a sentiment shared by British officers.

3. The fighting with the natives was far more personal to the Americans than anyone from Britian.

4. The British saw the American colonies as insignificant compared money sinks compared to the deeply lucrative colonies elsewhere.

5.1 Because gold and silver were so rare, bank notes backed by land and debts were practically the backbone of the American economy. This became a major issue when the British banks allowed borrowers to overleverage, as they passed laws to reduce the quantity of American notes, and bar their use as payment, while also reducing speice sent to America.

5.2 Needless to say, combining deflation with the mercantilist policies led to disaster dominos, since Spanish currency was even more common than British money before this, so increasing the imbalance further would almost certainly benefit those who were already breaking British laws.

6. Americans also had a tradition of getting what they wanted by rioting at this point, so the British decision to give their governors the soldiers they would actually need to prevent this came far too late.

So basically, there were a LOT of cultural differences by the time of the revolution.